Formula omitted]-labeling of disk intersection graphs

Abstract

In this paper we study the problem of L(2,1)-labeling of intersection graphs of disks. An L(2,1)-labeling is a mapping from the vertex set of the graph to non-negative integers, in which labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices at distance 2 are different. The span of an L(2,1)-labeling is the difference between the maximum and the minimum label used, and the span λ(G) of a graph G is the minimum span of an L(2,1)-labeling of G.We show that if G is an intersection graph of disks, then λ(G)≤45Δ2+25Δ+20. Moreover, if all disks in the geometric representation of G have equal radii, then λ(G)≤14Δ+11. We also present a refined upper bound for unit disk intersection graphs with small maximum degree.